On 17 Oct 2012, at 08:07, Russell Standish wrote:

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On Tue, Oct 16, 2012 at 03:39:18PM +0200, Bruno Marchal wrote:On 14 Oct 2012, at 23:27, Russell Standish wrote:On Sun, Oct 14, 2012 at 04:44:11PM -0400, Roger Clough wrote:"Computational Autopoetics" is a term I just coined to denote applying basic concepts of autopoetics to the field of comp. You mathematicians are free to do it more justice than I can. I cannot guarantee that the idea hasn't already been exploited, but I have seen no indication of that. The idea is this: that we borrow a basic characteristic of autopoetics, namely that life is essentially not a thing but the act of creation. This means that we define life as the creative act of generating structure from some input data. By this pramatic definition, it is not necessarily the structure that is produced that is alive, but life consists of the act of creating structure from assumedly structureless input data. Life is not a creation, but instead is the act of creation.So any self-organised system should be called alive then? Sanddunes,huricanes, stars, galaxies. Hey, we've just found ET!I am not sure a galaxy, or a sand dune has a "self", unlike a cell, or a person.You are, of course, correct that the self/other distinction is crucial to life (and also of evolution - there has to be a unit of selection - the replicator). I was responding initially to Roger's claim that life is the act of creating structure. Any self-organised system can do that.

Yes.

The self is directly related to the Dx = "xx" trick, for me.The Dx=xx trick is about self-replication. Of course entities with asenseof the self/other distinction needn't replicate (eg certain robots).

`Self-replication and self-reference. And many self-transformation (in`

`fact self-phi_i, for all i).`

`Self-reference and self-replication, are basically the same processes,`

`except that in replication you reproduce yourself relatively to some`

`universal numbers "grossly" different than you, (the most probable`

`physical world), and with self-reference you reproduce yourself`

`mentally, that is with respect to the universal number you are.`

Actually, I was just reading an interview with my old mate Charley Lineweaver in New Scientist, and he was saying the same thing :).If life is such a creative act rather than a creation, then it seems to fit what I have been postulating as the basic inseparable ingredients of life: intelligence and free will.I don't believe intelligence is required for creativity. Biological evolution is undeniably creative.Is life more creative than the Mandelbrot set?, or than any "creative set" in the sense of Post (proved equivalent with Turing universality)?I would say yes. The Mandelbrot set is self-similar, isn't it, so the coarse-grained information content must be bounded, no matter how far you zoom in.

`The M set is not just similar, the little M sets are surrounded by`

`more and more complex infiltration of their filaments. So the closer`

`you zoom, the more complex the set appears, and is, locally.`

`It is most plausibly a compact, bounded, version of a universal`

`dovetailer.`

Life, on the other hand, exhibits unbounded information through evolution, in contrast to all ALife simulations to date.

`To be fair you must look at some artificial evolution as long as life`

`evolution. And both the M set and all creative set, or subcreative,`

`(UD, UMs, LUMs, but also you and me, even without assuming comp) are`

`like that in their extensions. Unbounded complexity.`

`The M set is not only self-similar, but all its parts are similarly`

`self-similar, making all zoom repeated 2, 4, 8, 16, ... times when you`

`decide to focus on a minibrot.`

I had a look at the Wikipedia entry on creative sets, and it didn't make much sense, alas.

`OK. On the FOAR list, I will do soon, or a bit later, Church thesis,`

`the phi_i and the W_i, and that will give the material to get the`

`creative sets.`

`Roughly speaking, a creative set is a machine (a recursively`

`enumerable set of numbers) who complementary is constructively NOT`

`recursively enumerable. It is a machine defining a natural sort of no-`

`machine, capable to refute all attempt done by the machine to make it`

`into a machine.`

`john Myhill will prove that such set are equivalent (in some strong`

`sense) to the universal Turing set (machine).`

`If you remember the recursively enumerable set W_i,, and noting ~W_i`

`for ( N minus W_i), N = {0, 1, 2, 3, ...}`

`W_u is creative iff there is a computable function F producing, from y`

`and u, for all W_y contained in ~W_u, a number c in ~W_u minus W_y.`

`The attempt W_y of making ~W_u into a machine y, has failed, has now`

`we are given a counterexample, the number c, which is in ~W_u, and yet`

`not capture by W_y.`

`~W_u is called a productive set. It is a NON recursively enumerable`

`set (a non machine), but constructively so, as you can build a`

`transfinite approximation of it, in a communicable way, up to`

`omega_1^CK, (Church Kleene first non constructive ordinal), and beyond`

`(but at the machine risk and peril).`

`Truth, Arithmetical Truth, the set V of the Gödel numbers of the true`

`propositions, in (N, +, *) is a typical produce set. Gödel first`

`theorem is constructive: for all theories (recursively enumerbale`

`sets) attempting to get V, the Gödel diagonalization will provide a`

`Godel number of a proposition true but not in the theory (the set of`

`theorems of the theory). N minus Truth is also productive, Truth`

`cannot be isomorphic to the complementary of a creative machine.`

`Creative machine, or universal machine are sigma_1 complete, Truth is`

`sigma_i complete for all i!`

`Note that I identify here a number or a machine, and its set of`

`behaviors (input-output) or beliefs/theorems.`

More on this on FOAR asap :) Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.